Meanders: exact asymptotics Original Research Article

We conjecture that meanders are governed by the gravitational version of a c=−4 two-dimensional conformal field theory, allowing for exact predictions for the meander configuration exponent α=29(29+5)/12, and the semi-meander exponent ᾱ=1+11(29+5)/24. This result follows from an interpretation of meanders as pairs of fully packed loops on a random surface, described by two c=−2 free fields. The above values agree with recent numerical estimates. We generalize these results to a score of meandric numbers with various geometries and arbitrary loop fugacities.